Collective Dynamics from Stochastic Process Algebras

Precise interaction of individuals coupled with analysis of the dynamic behaviour at the level of populations.

Process calculi have traditionally been
discrete-state modelling tools. These
give precise characterisations of systems with a small number of
abstractly-described components. However,
such models cannot scale to large numbers of closely-described components. An alternative semantics
which is based on continuous-state representations can scale to describe large
populations of components but this comes at the cost of using an approximation
of the true (discrete) behaviour. Such continuous-state semantics have
been provided for the process algebra PEPA, and its recent biological dialect
Bio-PEPA. These have given rise to applications in software systems,
scalability analyses, systems biology, epidemiology and crowd dynamics.

There is potential for several
PhD projects arising from this theme.
For example, the feasibility of developing good models of collective
behaviour for systems with distinct spatial compartments or regions is yet to
be fully explored. There is also several
interesting questions with respect to heterogenous systems in which only some
subpopulations scale uniformly but which nevertheless exhibit collective
behaviour overall. Another example,
would be the development of suitable query languages and logics to interrogate
the behaviour of such systems.